**Abstract**

The work discussed shortly the experimental results, which was the waveguide-resonance mechanism relevation forerunner of characteristic X-ray radiation flux propagation. Technology of the planar air extended slit clearance preparation is presented. The methodology of X-ray beam parameter study formed by these slit clearances, which allowed to find the critical parameter answering for the radiation flux propagation mechanism change from the multiple external total reflections to the waveguide-resonance one, is described. Main features of the X-ray flux waveguideresonance propagation mechanism were revealed. The self-consistent model of the mechanism is displayed with details. It is shown that the waveguide-resonance effect has universal character, and it reflects the fundamental nature phenomenon. The peculiarities of X-ray device functioned in frame of the phenomenon manifestation planar X-ray waveguide resonator (PXWR) and the increasing methods of its practical efficiency are discussed. The phenomenon practical application is presented concisely.

**Keywords:** X-ray flux, external total reflection, X-ray standing wave, coherence length, X-ray nanophotonics, planar X-ray waveguide resonator, waveguide-resonance propagation phenomenon, spatial coherence, angular divergence, partial angular tunneling effect

#### **1. Introduction**

The problem of X-ray beam formation with a minimal size cross section and a small angular divergence is the central problem of all X-ray diagnostical methods. The first real step for the solution of this problem was connected with the names of P. Hirsch and J. Keller suggested to form X-ray microbeams by employing the glass capillary [1]. More recently, the planar thin film waveguides have been offered for X-ray microbeam formation [2]. Authors of the work showed that the waveguide with a material media core for X-ray beam transportation can form small size beams, but the beam intensity attenuation was very great. In the direction, development similar investigations were carried out in a number of experimental works

[3–5]. Authors of these investigations have managed to obtain X-ray beams with a width of 100 nm, a height of some millimeters, and the total intensity near <sup>5</sup> <sup>10</sup><sup>7</sup> photon/s in condition of the resonant synchrotron radiation coupling. The significant progress in these research works was achieved by switching over a study from coupling mechanism of the emergent beam preparation to the ones based on the radiation transportation by the core layer from input of the waveguide to its outlet. In result of the flux mode structure analysis, the phenomenon of an X-ray standing wave arising was mentioned [4]. The properties of X-ray beams formed by polycapillary optics systems have been intensively studied, too [6–10]. The optics of systems is based on the phenomenon of X-ray beam multiple total external reflections on the inner surface of a quartz capillary. Mono and polycapillary optics are the beautiful facilities for the formation of microsize beams. At the same time, the polycapillary optics is characterized by significant losses of X-ray beam intensity in the transportation process. The problem of X-ray flux intensity losses was the subject of a specific investigation [11]. Authors of the work studied the effect of capillary damages in result of X-ray beam influence. They demonstrated the linear worsening of X-ray beam transmission ability for the glass capillary with an increase of radiation dose. This effect is not significant for the quartz guides of X-ray fluxes.

Materials with information about Δλ magnitudes featured for X-ray characteristic radiation produced by X-ray laboratory sources are presented in Handbook editions [27, 28]. But the main shortage at interpretation of X-ray flux transportation by different waveguide structures including slitless collimator devices was the statement that X-ray flux propagation takes place accordingly to the multiple total external reflection mechanisms as sole possible one. We were skeptical of this point of view and decided to produce the systematic investigation of the planar extended slit clearance width influence on its X-ray emergent beam parameters. For similar investigations, we selected construction presented in **Figure 1**. It is the air planar

*Scheme of X-ray initial flux capture area and the emergent beam formation by the planar extended slit clearance formed by two quartz reflectors (a) and real construction of the device for the study of the spatial intensity distribution dependence in X-ray beams on the slit clearance width (b). 1: aligning handles; 2: installation plate; 3: spring pawls; 4: fine tuning screws; 5: radiation guide holder; 6: quartz reflectors with*

*Radiation Fluxes Waveguide-Resonance Phenomenon Discovered in Result of X-Ray Nanosize…*

The main components of the PXW structure are planar polished dielectric reflectors forming its radiation-transporting air slit clearance. In preparation of reflector working surfaces, it is necessary to fulfill a number of technological requirements guaranteeing the desired surface quality. The technical parameters that determine the surface quality are first of all the roughness and waviness and, moreover, a specific factor associated with local work hardening arising from

Modern polishing methods are capable of ensuring a surface roughness level of about 0.5 nm. Such a high degree of polishing can be controlled via direct testing with the help of atomic-force microscopy. The aforementioned roughness level is quite comparable with the range within which the potential on the condensed material surface varies from the value typical of its entire volume to that

corresponding to vacuum [29, 30]. At the same time, the atomic-force microscopy technique makes it impossible to estimate the surface waviness and, moreover, the level and degree of surface distortions caused by the appearance of local work hardening. To a certain extent, the influence of these parameters on the surface quality can be estimated with the help of an optical method based on violated total internal reflection [31], which enables us to discard reflectors with appreciable

In preparation of waveguide resonators, the most critical technological stage is

thin film metallic strip deposition on the edges of one of the quartz reflectors constituting a pair used to create a waveguide-resonance channel. The deposited materials are titanium or chromium with a high degree of adhesion to the quartz surface. During the deposition process, the surface of the future waveguide-resonance

contributions to the deterioration of the reflector surface quality.

extended X-ray waveguide (PXW).

**Figure 1.**

**147**

**2. Technological features of PXW fabrication**

*length 100 mm; h and s: height and width of slit clearance (φ<sup>1</sup> = φ2).*

*DOI: http://dx.doi.org/10.5772/intechopen.93174*

nonuniform surface heating during polishing.

In parallel with the traditional approaches to micron and submicron X-ray beam formation mentioned above, it has been discovered the specific technique of a superfine beam preparation by using the so-called "slitless" collimator [12–14] formed by two quartz plane polished plates mated together. Its device lets to form X-ray emergent beam with the visible magnitude of a radiation intensity compared with the incident beam intensity value [12]. Unfortunately, the study of this phenomenon and attempts of its practical application have been undertaken in recent years only [15, 16]. In fact, the slitless X-ray collimator represents the planar waveguide with a minimum size of an air slit. Width of the slit is defined by roughness and waviness levels of the collimator reflector plane surfaces. At the same time, the air core between guide claddings is the ideal waveguide channel from standpoint of the radiation flux intensity preservation. Similar waveguides with fixed and tunable air gaps have begun to find the practical application in the works of Zwanenburg group [17, 18]. Their waveguides with Cr claddings and air core can produce the emergent beam with a width of *d* = 500 nm, a height of *h* = 0.1 mm, and a total intensity of *<sup>J</sup>* = 2.4 <sup>10</sup><sup>7</sup> photon/s [17]. Great omission of these works consisted in the ignoration of X-ray standing wave arising in air core of their radiation guides.

The original glance on the problem of X-ray flux transportation by a planar extended slit clearance was presented in the works of Kawai group [19]. As opposite to the standing wave conception, authors included the specific notion about X-ray traveling waves or Yoneda wing. This approach has some grounding in theory [20, 21]. But these works left behind bracket the interference interaction between falling and reflecting fluxes.

Very strange approach was suggested by Dabagov for the description of X-ray flux transportation by a hollow quartz capillary [22]. Instead of the conventional conception connected with the multiple total external reflection mechanisms, author advanced the idea of "X-ray quantum subsurface channeling." We believe that the approach is not pragmatic since the channeling phenomenon offers a photon motion in the periodic potential, but the surface of amorphous quartz cannot produce the correct periodic field.

A number of publications with model description attempts of X-ray flux propagation through a narrow extended slit are presented in the literature [23–26]. These models are built on the working hypothesis that X-ray radiation is the planar monochromatic electromagnetic wave. But it is universally known that the realistic X-ray sources produce the quasimonochromatic radiation fluxes with λ<sup>0</sup> average wavelength and Δλ monochromatism degree.

*Radiation Fluxes Waveguide-Resonance Phenomenon Discovered in Result of X-Ray Nanosize… DOI: http://dx.doi.org/10.5772/intechopen.93174*

#### **Figure 1.**

[3–5]. Authors of these investigations have managed to obtain X-ray beams with a width of 100 nm, a height of some millimeters, and the total intensity near <sup>5</sup> <sup>10</sup><sup>7</sup> photon/s in condition of the resonant synchrotron radiation coupling. The significant progress in these research works was achieved by switching over a study from coupling mechanism of the emergent beam preparation to the ones based on the radiation transportation by the core layer from input of the waveguide to its outlet. In result of the flux mode structure analysis, the phenomenon of an X-ray standing wave arising was mentioned [4]. The properties of X-ray beams formed by polycapillary optics systems have been intensively studied, too [6–10]. The optics of systems is based on the phenomenon of X-ray beam multiple total external reflections on the inner surface of a quartz capillary. Mono and polycapillary optics are the beautiful facilities for the formation of microsize beams. At the same time, the polycapillary optics is characterized by significant losses of X-ray beam intensity in the transportation process. The problem of X-ray flux intensity losses was the subject of a specific investigation [11]. Authors of the work studied the effect of capillary damages in result of X-ray beam influence. They demonstrated the linear worsening of X-ray beam transmission ability for the glass capillary with an increase of radiation dose. This effect is not significant for the quartz guides of X-ray fluxes. In parallel with the traditional approaches to micron and submicron X-ray beam

*Electromagnetic Propagation and Waveguides in Photonics and Microwave Engineering*

formation mentioned above, it has been discovered the specific technique of a superfine beam preparation by using the so-called "slitless" collimator [12–14] formed by two quartz plane polished plates mated together. Its device lets to form X-ray emergent beam with the visible magnitude of a radiation intensity compared with the incident beam intensity value [12]. Unfortunately, the study of this phenomenon and attempts of its practical application have been undertaken in recent years only [15, 16]. In fact, the slitless X-ray collimator represents the planar waveguide with a minimum size of an air slit. Width of the slit is defined by roughness and waviness levels of the collimator reflector plane surfaces. At the same time, the air core between guide claddings is the ideal waveguide channel from standpoint of the radiation flux intensity preservation. Similar waveguides with fixed and tunable air gaps have begun to find the practical application in the works of Zwanenburg group [17, 18]. Their waveguides with Cr claddings and air core can produce the emergent beam with a width of *d* = 500 nm, a height of *h* = 0.1 mm, and a total intensity of *<sup>J</sup>* = 2.4 <sup>10</sup><sup>7</sup> photon/s [17]. Great omission of these works consisted in the ignoration of X-ray standing wave arising in air core of their radiation guides. The original glance on the problem of X-ray flux transportation by a planar extended slit clearance was presented in the works of Kawai group [19]. As opposite to the standing wave conception, authors included the specific notion about X-ray traveling waves or Yoneda wing. This approach has some grounding in theory [20, 21]. But these works left behind bracket the interference interaction between

Very strange approach was suggested by Dabagov for the description of X-ray flux transportation by a hollow quartz capillary [22]. Instead of the conventional conception connected with the multiple total external reflection mechanisms, author advanced the idea of "X-ray quantum subsurface channeling." We believe that the approach is not pragmatic since the channeling phenomenon offers a photon motion in the periodic potential, but the surface of amorphous quartz

A number of publications with model description attempts of X-ray flux propagation through a narrow extended slit are presented in the literature [23–26]. These models are built on the working hypothesis that X-ray radiation is the planar monochromatic electromagnetic wave. But it is universally known that the realistic X-ray sources produce the quasimonochromatic radiation fluxes with λ<sup>0</sup> average

falling and reflecting fluxes.

**146**

cannot produce the correct periodic field.

wavelength and Δλ monochromatism degree.

*Scheme of X-ray initial flux capture area and the emergent beam formation by the planar extended slit clearance formed by two quartz reflectors (a) and real construction of the device for the study of the spatial intensity distribution dependence in X-ray beams on the slit clearance width (b). 1: aligning handles; 2: installation plate; 3: spring pawls; 4: fine tuning screws; 5: radiation guide holder; 6: quartz reflectors with length 100 mm; h and s: height and width of slit clearance (φ<sup>1</sup> = φ2).*

Materials with information about Δλ magnitudes featured for X-ray characteristic radiation produced by X-ray laboratory sources are presented in Handbook editions [27, 28]. But the main shortage at interpretation of X-ray flux transportation by different waveguide structures including slitless collimator devices was the statement that X-ray flux propagation takes place accordingly to the multiple total external reflection mechanisms as sole possible one. We were skeptical of this point of view and decided to produce the systematic investigation of the planar extended slit clearance width influence on its X-ray emergent beam parameters. For similar investigations, we selected construction presented in **Figure 1**. It is the air planar extended X-ray waveguide (PXW).

### **2. Technological features of PXW fabrication**

The main components of the PXW structure are planar polished dielectric reflectors forming its radiation-transporting air slit clearance. In preparation of reflector working surfaces, it is necessary to fulfill a number of technological requirements guaranteeing the desired surface quality. The technical parameters that determine the surface quality are first of all the roughness and waviness and, moreover, a specific factor associated with local work hardening arising from nonuniform surface heating during polishing.

Modern polishing methods are capable of ensuring a surface roughness level of about 0.5 nm. Such a high degree of polishing can be controlled via direct testing with the help of atomic-force microscopy. The aforementioned roughness level is quite comparable with the range within which the potential on the condensed material surface varies from the value typical of its entire volume to that corresponding to vacuum [29, 30]. At the same time, the atomic-force microscopy technique makes it impossible to estimate the surface waviness and, moreover, the level and degree of surface distortions caused by the appearance of local work hardening. To a certain extent, the influence of these parameters on the surface quality can be estimated with the help of an optical method based on violated total internal reflection [31], which enables us to discard reflectors with appreciable contributions to the deterioration of the reflector surface quality.

In preparation of waveguide resonators, the most critical technological stage is thin film metallic strip deposition on the edges of one of the quartz reflectors constituting a pair used to create a waveguide-resonance channel. The deposited materials are titanium or chromium with a high degree of adhesion to the quartz surface. During the deposition process, the surface of the future waveguide-resonance channel was coated with aluminum foil. Thin film metallic strips were primarily deposited in the vacuum chamber of a Leybord LG L-560 setup via the electron beam evaporation method. The film coating growth rate was 0.1 nm/s. During the deposition process, the chamber pressure was maintained at a level of 10<sup>4</sup> Pa. However, in spite of relatively high vacuum, the metallic-strip material contained a certain number of oxygen atoms (up to 10 at%). When the films were deposited, some reflectors were heated up to 80°C. As a result, the density of coating adhesion to the quartz glass surface increased appreciably. A simplified diagram of the mutual arrangement of assemblies in the chamber used to the deposit coatings in vacuum is depicted in **Figure 2**. The position of the reflector intended for coating deposition is symmetric with respect to the point source of metal atoms.

The basic requirement to the quality of the prepared strip coatings is thickness homogeneity along the entire length of the PXW reflector. Let us consider the geometry of the diagram, as shown in **Figure 2**. Then, under the assumption of angular homogeneity of the metal atom flux excited by the electron beam, it can be expected that the deposited strips will be characterized by a nonuniform coating thickness and its largest value will be at the reflector center. For coating deposition condition optimization, it is necessary to employ the thickness control methods. At the center (*t2*) and edges (*t1*) of the reflector (**Figure 3**), the deposited strip thicknesses were determined via the Rutherford backscattering (RBS) of Не<sup>+</sup> ions with the help of "blank samples." Single-crystal silicon samples located on aluminum foil, which covered the surface during deposition, were used as these blank samples. Thus, each reflector with deposited metallic coatings can be characterized by at least two Ti/Si blank samples. Their experimental investigations were performed by means of the Sokol-3 ion beam analytical complex situated at the Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences [32]. The results of these measurements are depicted in **Figure 4**.

Using the spectra of the RBS of Не<sup>+</sup> ions (*E*<sup>0</sup> = 1 MeV) (**Figure 4**), it is possible to perform accurate determination of the thicknesses of the strips deposited on reflectors in their central part (**Figure 4a**) and on the edges (**Figure 4b**). These thicknesses are determined by approximating peaks with almost flat tops, which

correspond to Не<sup>+</sup> ion scattering from the coating atoms. (The low energy steps observed in the RBS spectra of the tested targets correspond to Не<sup>+</sup> ion scattering from substrate atoms.) The presented spectra were mathematically processed using RUMPP, the modified version of the famous RUMP approximation program [33]. Approximation of the aforementioned spectra indicates that the film strip thicknesses are *t*<sup>2</sup> = 114 0.5 nm in the central part and *t*<sup>1</sup> = 107.5 0.5 nm on the edges. Thus, the inhomogeneity in the thickness of the strips deposited onto the given reflector is 6%. This result completely coincides with the estimate based on geometric considerations. The above data correspond to the reflector whose coatings were deposited at a distance of *h* = 200 mm between the source of the evaporated atoms and its surface (**Figure 2**). The reflector length is *l* = 100 mm. Under the assumption that the deposition rate is proportional to the squared distance from the source, the expected difference turns out to be 6.1%. For the coating thickness difference decreasing, we increased the *h*-distance up to 1000 mm. In that case, the thickness difference accordingly to RBS data achieved to 1%. Experiments showed

*Typical spectra of the RBS of Не<sup>+</sup> ions (*Е<sup>0</sup> *= 1 MeV). Data were obtained for Ti/Si blank samples located at the positions* А *and* В *(Figure 2) corresponding to the (a) edge and (b) center of the strip coatings of the quartz*

*Waveguide-resonator reflector with thin film strips on the edges: t1 and are the coating thicknesses on its edges,*

*Radiation Fluxes Waveguide-Resonance Phenomenon Discovered in Result of X-Ray Nanosize…*

**Figure 3.**

**Figure 4.**

*reflectors.*

**149**

*and t2 is the thickness in the central part.*

*DOI: http://dx.doi.org/10.5772/intechopen.93174*

that the similar conditions are acceptable for X-ray waveguide assemblage.

Specific attention has been given to the direct determination of the effective slit width in different waveguides and in a slitless collimator because the data presented in early works about slitless devices [12–14] were not clear with respect to the width. The width was evaluated by very effective optical method connected with the attenuated total internal reflection effect [31]. In our investigation, we used the laser source with λ<sup>0</sup> = 680 nm. **Figure 5** presents the measurement geometry. The studied waveguide was situated in a specific cartridge equipped by black light absorber. The light beam introduced into the waveguide by using the quartz prism

#### **Figure 2.**

*Simplified diagram of the chamber used to deposit titanium strips on quartz reflectors: (1) electron gun, (2) focusing system, (3) titanium target, (4) quartz reflector, (5) vacuum volume,* h *= 200 mm,* l *= 100 mm; and* A *and* B *are the positions of blank samples during deposition.*

*Radiation Fluxes Waveguide-Resonance Phenomenon Discovered in Result of X-Ray Nanosize… DOI: http://dx.doi.org/10.5772/intechopen.93174*

#### **Figure 3.**

channel was coated with aluminum foil. Thin film metallic strips were primarily deposited in the vacuum chamber of a Leybord LG L-560 setup via the electron beam evaporation method. The film coating growth rate was 0.1 nm/s. During the deposition process, the chamber pressure was maintained at a level of 10<sup>4</sup> Pa. However, in spite of relatively high vacuum, the metallic-strip material contained a certain number of oxygen atoms (up to 10 at%). When the films were deposited, some reflectors were heated up to 80°C. As a result, the density of coating adhesion to the quartz glass surface increased appreciably. A simplified diagram of the mutual arrangement of assemblies in the chamber used to the deposit coatings in vacuum is depicted in **Figure 2**. The position of the reflector intended for coating deposition is symmetric with respect to the point source of

*Electromagnetic Propagation and Waveguides in Photonics and Microwave Engineering*

The basic requirement to the quality of the prepared strip coatings is thickness homogeneity along the entire length of the PXW reflector. Let us consider the geometry of the diagram, as shown in **Figure 2**. Then, under the assumption of angular homogeneity of the metal atom flux excited by the electron beam, it can be expected that the deposited strips will be characterized by a nonuniform coating thickness and its largest value will be at the reflector center. For coating deposition condition optimization, it is necessary to employ the thickness control methods. At the center (*t2*) and edges (*t1*) of the reflector (**Figure 3**), the deposited strip thicknesses were determined via the Rutherford backscattering (RBS) of Не<sup>+</sup> ions with the help of "blank samples." Single-crystal silicon samples located on aluminum foil, which covered the surface during deposition, were used as these blank samples. Thus, each reflector with deposited metallic coatings can be characterized by at least two Ti/Si blank samples. Their experimental investigations were performed by means of the Sokol-3 ion beam analytical complex situated at the Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences [32]. The results of these measurements are depicted in **Figure 4**.

Using the spectra of the RBS of Не<sup>+</sup> ions (*E*<sup>0</sup> = 1 MeV) (**Figure 4**), it is possible to perform accurate determination of the thicknesses of the strips deposited on reflectors in their central part (**Figure 4a**) and on the edges (**Figure 4b**). These thicknesses are determined by approximating peaks with almost flat tops, which

*Simplified diagram of the chamber used to deposit titanium strips on quartz reflectors: (1) electron gun, (2) focusing system, (3) titanium target, (4) quartz reflector, (5) vacuum volume,* h *= 200 mm,* l *= 100 mm; and*

A *and* B *are the positions of blank samples during deposition.*

metal atoms.

**Figure 2.**

**148**

*Waveguide-resonator reflector with thin film strips on the edges: t1 and are the coating thicknesses on its edges, and t2 is the thickness in the central part.*

#### **Figure 4.**

*Typical spectra of the RBS of Не<sup>+</sup> ions (*Е<sup>0</sup> *= 1 MeV). Data were obtained for Ti/Si blank samples located at the positions* А *and* В *(Figure 2) corresponding to the (a) edge and (b) center of the strip coatings of the quartz reflectors.*

correspond to Не<sup>+</sup> ion scattering from the coating atoms. (The low energy steps observed in the RBS spectra of the tested targets correspond to Не<sup>+</sup> ion scattering from substrate atoms.) The presented spectra were mathematically processed using RUMPP, the modified version of the famous RUMP approximation program [33]. Approximation of the aforementioned spectra indicates that the film strip thicknesses are *t*<sup>2</sup> = 114 0.5 nm in the central part and *t*<sup>1</sup> = 107.5 0.5 nm on the edges. Thus, the inhomogeneity in the thickness of the strips deposited onto the given reflector is 6%. This result completely coincides with the estimate based on geometric considerations. The above data correspond to the reflector whose coatings were deposited at a distance of *h* = 200 mm between the source of the evaporated atoms and its surface (**Figure 2**). The reflector length is *l* = 100 mm. Under the assumption that the deposition rate is proportional to the squared distance from the source, the expected difference turns out to be 6.1%. For the coating thickness difference decreasing, we increased the *h*-distance up to 1000 mm. In that case, the thickness difference accordingly to RBS data achieved to 1%. Experiments showed that the similar conditions are acceptable for X-ray waveguide assemblage.

Specific attention has been given to the direct determination of the effective slit width in different waveguides and in a slitless collimator because the data presented in early works about slitless devices [12–14] were not clear with respect to the width. The width was evaluated by very effective optical method connected with the attenuated total internal reflection effect [31]. In our investigation, we used the laser source with λ<sup>0</sup> = 680 nm. **Figure 5** presents the measurement geometry. The studied waveguide was situated in a specific cartridge equipped by black light absorber. The light beam introduced into the waveguide by using the quartz prism

**3. Experimental setup for the radiation intensity distribution study**

*Radiation Fluxes Waveguide-Resonance Phenomenon Discovered in Result of X-Ray Nanosize…*

part of initial X-ray spectra only.

*DOI: http://dx.doi.org/10.5772/intechopen.93174*

*beams formed by quartz planar waveguides.*

**Figure 7.**

**151**

**4. Angular radiation intensity distribution in X-ray beams**

In the course of our measurements, the waveguide position in experimental setup in experimental process was not changed. In the experimental process, the distance between the waveguide inlet and the X-ray tube focal position was 75 mm, and the distance between the waveguide outlet and the X-ray detector slit was 460 mm. X-ray flux capture angle calculated on the basis of geometric approach was equal to 0.08° owing to the size of tube focus projection evaluated as 0.1 mm. In experiments, the diffractometer angular step Δ(2θ) was 0.02°. At the same time,

*Instrumental facility for the spatial distribution study of a quasimonochromatic radiation intensity in X-ray*

The main device to study the X-ray intensity distribution was the HZG-4 diffractometer manufactured by Carl Zeiss Jena Firm. We produced some modification of the device by its detector circle radius increasing up to 500 mm. In the modification result, the measurement space resolution improved in three times. The measurement spectroscopic circuit was completed by NIM standard units produced by Ortec firm. The shaping time of amplifier unit was selected as 0.5 μs. Such selection allowed to get the pulse registration count rate up to 100 kHz. The design of our registration setup is presented in **Figure 7**. X-ray diffractometer used as the setup background is characterized by scanning regimes in nonstop function and start-stop moving with a minimum step of δ(2θ) = 0.001°. X-ray detector was equipped by slit-cut arrester with a width of *s* = 0.1 mm and a height of *h* = 10 mm and Soller slit system limiting the registered flux vertical divergence by value near 2°. X-ray flux take-off angle was selected near 6°. Main volume of experimental investigations was executed by X-ray tube BSW-24 (Cu) in regime *U* = 20 keV and *I* = 10 mA. Similar tube with Fe anode was exploited in some selective measurements. The X-ray space intensity distribution data collection was produced with the use of Cu filter attenuator characterized by the CuKα radiation decreasing factor *K* = 200. For the energy spectrum characterization, our facility setup was equipped by a pulse multichannel analyzer ACCUSPEC Canberra Packard in the form of PC computer board. In measurements of PXW parameters, we used the characteristic

**Figure 5.**

*Principle scheme for direct measurements of a waveguide slit width by methods of the attenuated internal total reflection (AITR). I and II are quartz reflectors of a waveguide. Scheme was published, in first, in Ref. [34].*

**Figure 6.**

*Experimental data presented the relationship between the waveguide slit width and the reflectivity magnitude are obtained by AITR method. The point characterized the slitless collimator has a specific design.*

fixed on the waveguide reflector by specific oil (*n* = 1.45). The prism could change its position on the reflector surface. Emergent light beam in the measurement process registered by standard photodiode equipped by circular aperture with a diameter of *d* = 0.5 mm. In the measurements process, the light beam in transit through the prism incidented on the waveguide, underwent the attenuated total internal reflection on the waveguide slit clearance and a lux meter recorded the reflection intensity. The normalization measurement was executed by using the waveguide with a width slit of *s* = 0.12 mm. Specific details of investigations are described elsewhere [34]. The measured data for several waveguides with different slit widths are presented in **Figure 6**.

Standard least square method was used for the experimental data fitting allowed to get a relationship between the light beam reflectivity factor and the width of waveguide slit clearance. In process of the slitless collimator study, we registered the gap width variation in interval 0–60 nm at the prism translation along the slitless unit. In result, we concluded that the slitless collimator is characterized by effective width of the gap *s* = 30 30 nm.

*Radiation Fluxes Waveguide-Resonance Phenomenon Discovered in Result of X-Ray Nanosize… DOI: http://dx.doi.org/10.5772/intechopen.93174*
